Vector and matrix transpose

A column vector:
\[
\mathbf{v} =
\begin{bmatrix}
v_1 \\
v_2 \\
v_3
\end{bmatrix}
\]

Transposed to a row vector:
\[
\mathbf{v}^T =
\begin{bmatrix}
v_1 & v_2 & v_3
\end{bmatrix}
\]

Which is equivalent to:
\[
\mathbf{\begin{bmatrix}
v_1 \\
v_2 \\
v_3
\end{bmatrix}}^T =
\begin{bmatrix}
v_1 & v_2 & v_3
\end{bmatrix}
\]
And:
\[
\mathbf{\begin{bmatrix}
v_1 & v_2 & v_3
\end{bmatrix}}^T =
\begin{bmatrix}
v_1 \\
v_2 \\
v_3
\end{bmatrix}
\]

And for a double/multiple column vector transposed to a row vector:

\[
\mathbf{\begin{bmatrix}
v_1 & v_4 \\
v_2 & v_5 \\
v_3 & v_6
\end{bmatrix}}^T =
\begin{bmatrix}
v_1 & v_2 & v_3 \\
v_4 & v_5 & v_6
\end{bmatrix}^T =
\begin{bmatrix}
v_1 & v_4 \\
v_2 & v_5 \\
v_3 & v_6
\end{bmatrix}
\]

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